ACCOUNTS OF CHEXICAL RESEARCH VOLUME 12
NUMBER 8
AUGUST, 1979
Relativistic Effects on Chemical Properties KENNETHS. PITZER Department of Chemistry and Lawrence Berkeley Laboratory, University of California, Berkeley, California 94720 Received November 8. 1978
While it is generally recognized that a rigorous theoretical foundation for chemistry would rest on relativistic quantum theory, the great majority of quantum mechanical calculations of quantities of chemical interest are based on the nonrelativistic Schrodinger equation, or its equivalent, together with the qualitative rules related to spin and the Pauli exclusion principle. If fine structure features are of interest, spin-orbit, spin-spin, and other terms are added as perturbations, but for light atoms these terms yield very small energies that may be of spectroscopic interest but have no effect on most chemical properties. For very heavy atoms, however, this situation changes. Certain terms which were very small compared to thermal energy for light atoms increase very rapidly with atomic number and become comparable to chemical bond energies for elements in the range gold-bismuth. The most familiar relativistic property is probably the increase in particle mass as the velocity approaches that of light. It is the s electrons with no orbital angular momentum that approach the nucleus most closely and therefore gain the highest velocity. For these heavy atoms the inner 1s and 2s electrons have average velocities close enough to that of light to have a substantial increase in mass. As a result these electrons spend even more time near the nucleus, have contracted mean radii, and have orbital energies which are increased (more negative). With this contraction of the inner s shells, outer s electrons also get closer to the nucleus and are affected in the same way. The relativistic effects on p, d, and f electrons are more complex and will be discussed below. But the essential result is that calculations based on the Schrodinger equation are not adequate for a discussion of the chemical properties of heavy atoms. Also extrapolations downward in the periodic table for the properties of possible superheavy elements are very hazardous since these relativistic effects increase very rapidly with Kenneth S. Pitzer, born in 1914 in Pomona, CA, received his B.S. from the California Institute of Technology and his Ph.D. from the University of California, Berkeley. He is a member of the faculty at Berkeley, having served in that capacity from 1937 to 1961 arid again since 1971. He has also hekl various administrative positions including that of Director of Research for the U.S. Atomic Energy Commission (1949-1951), President of Rice University (1961-1968), arid President of Stanford University (1968-1970). His research interests include thermodynamics, statistical mechanics, and quantum mechanics as applied to chemistry, as well as experimental work in spectroscopy and thermochemistry.
0001-4842/79/0112-0271$01.00/0
Table I Energy Terms for Fourth Group Elements (Electronvolts) element
X C Si Ge Sn Pb
‘
ionization potential 11.26 8.15 7.88 7.34 7.42
X, bond
spin-orbit
Do
3P,-3P0
6.1 3.2 2.8 2.0 1.0
0.005 .03 .17 .42 1.32
increase in atomic number. My principal purpose in this Account is to examine the special or anomalous chemical effects that have been noted for heavy elements in relation to periodic-table trends and to determine the degree to which these are relativistic effects. To the extent that these anomalies are explained in most inorganic chemistry books, they are usually ascribed to the introduction of the 4f shell. It is found that the effects of the 4f shell and the effects of relativity are of comparable magnitude, with the latter becoming more important for elements substantially heavier than the lanthanides. The mathematical structure of relativistic quantum mechanics1 is considerably more complex than that of the nonrelativistic theory; hence, one uses fully relativistic theory based on the Dirac equation only when it is needed. For work with elements of intermediate atomic number, there is a well-developed perturbation theory, due largely to Pauli, which allows one to examine the various relativistic terms on the basis of the Schrodinger wavefunctions and to include those corrections which may be significant in a particular situation. But for very heavy elements the validity, or even the convenience, of this perturbation approach is doubtful, and it is better to start with the Dirac equation. After submitting the initial version of this Account I learned of the Account of Pyykko and Desclaux2which is being published simultaneously. These authors outline the mathematical formulation of relativistic quantum theory, including the Dirac equation; hence the corresponding material has been deleted from the present paper. Also available is a more detailed review by Pyykko3 with an extensive bibliography. (1) See, for example, H. A. Bethe and E. E. Salpeter, “Quantum Mechanics of One- and Two-Electron Atoms”, Academic Press, New York, 1957; or I. P. Grant, Adu. Phys., 19, 747 (1970). (2) P. Pyykko and J. P. Desclaux, Acc. Chem. Res., 12, 271 (1979).
0 1979 American Chemical Society
272
Pitzer
In a sense the spin of electrons and other particles and the exclusion principle are themselves relativistic effects in that they are integral parts of relativistic quantum theory whereas they are appended as separate postulates in the conventional theory which starts with the Schrodinger equation. But the effects arising from spin alone or from the exclusion principle are not the subject of this Account; indeed they are part of conventional “nonrelativistic” theory. The spin-orbit energy, which is often mentioned as an effect splitting spectral lines, is a relativistic effect in our present sense and is one of those terms which becomes large for heavy elements. Indeed it is convenient to take this spin-orbit energy as a measure of the need to use relativistic theory for chemical phenomena. In Table I the spinorbit energies are compared with ionization potentials and bond dissociation energies for the fourth group elements. A chemical bond energy for relatively large atoms is roughly 2 eV (46 kcal or 190 kJ). From Table I we see that the spin-orbit term is small compar.ed to a chemical bond energy for fourth group elements through tin but becomes larger than the bond energy in lead, Also there is an anomalous drop in the bond energy for lead below that of any reasonable extrapolation of the trend from silicon to germanium to tin. This illustrates the hazard in a simple extrapolation for the bond energy of eka-lead, element 114, which is of interest as a possible synthetic superheavy elementa4 From data such as that in Table I, one can estimate that the perturbation approach starting with nonrelativistic theory will probably suffice through elements such as tin for chemical bonding calculations as well as for spin-orbit energies, but that for heavier elements one should use fully relativistic theory. Experience to date on molecular calculations is in agreement with that estimate. Let us turn now to a more comprehensive consideration of the anomalous effects that have been noted for heavy elements. Cotton and Wilkinson15in their third edition of “Advanced Inorganic Chemistry”, do not mention relativistic effects explicitly, but they do note: (1)the lanthanide contraction, (2) the inert pair effect, (3) the unique properties of gold (as compared to Ag and Cu), of mercury (as compared to Cd and Zn), and of Uvl, NpV1,and Puvl (as compared to the corresponding lanthanides), and (4)the effect on magnetic properties of the large spin-orbit interaction in compounds of Os1”, etc. Let us consider first the role of relativity as compared to other possible factors for (1) through (3). The spin-orbit effect in (4) is purely relativistic, and we shall subsequently comment briefly on it. We consider first the conclusions that can be drawn from comparisons of relativistic and nonrelativistic calculations for atoms. There are complete tables of self-consistent-field calculations6-8 yielding orbital (3) P. Pyykko, Adu. Quantum Chem., 11, 353 (1978). (4) G. T. Seaborg, W. Loveland, and D. J. Morrissey, Science, 203, ’ill 11979). (5) F. A. Cotton and G. Wilkinson, “Advanced Inorganic Chemistry”, 3rd ed., Interscience, New York, 1972. (6) J. P. Desclaux, Atom. Data Nucl. Data, 12, 311 (1973). (7) J. B. Mann, Los Alamos Laboratory Reports LA-3690 (1967) and LA-3691 (1968). (8) C. Froese Fisher, Atom. Data, 4,301 (1972);Atom. Data Nucl. Data. 12, 87 (1973).
Accounts of Chemical Research
Table I1 Lanthanide Contradion: 5p Mean Radii (4p for Yttrium) and Observed Ionic Radii ( A )
Y La
Lu
nonrel
calculated ( r ) av re1 D,,*
0.778 0,970 0.774
0.774 0.958 0.745
0.779 0.971 0.764
D, ,~
observed ionic radius
0.763 0.931 0.706
0.88 1.061 0.848
energies, radii of the various orbitals, and other properties. Also the orbital energies are approximately related to experimental ionization potential^.^ Thus it is convenient to use this information concerning the atoms to a maximum extent. Not very many relativistic calculations have been made, as yet, for the electronic motion in molecules. In a later section a few of these calculations, which yield results of general chemical interest, will be considered, but we make no pretense of giving a complete account of all relativistic calculations on the electronic structure of atoms and molecules. Conclustions Based on Atomic Properties In addition to atomic spectral data we have complete tables from Desclaux6 based on solution of the Dirac equation and yielding orbital energies, radii, and other properties. Comparable nonrelativistic tables are available from several source^.^^^ Except for s orbitals, where there is no orbital angular momentum, the spin-orbit interaction divides a shell of a given 1 into subshells with total angular momentum j = 1 - ‘/2 and j = 1 + 1/2. Relativistic calculations yield separate energies and radii for each subshell. The difference in energy is just the spin-orbit energy. Where it is appropriate to average the properties of the subshells, they are weighted as 2.1’+ 1. Electronic velocities are highest in the region close to the nucleus. Thus it is not surprising that relativistic effects are greatest for s orbitals which have the greatest density near the nucleus and in the direction of decreasing the radius and increasing the ionization potential. The effect on p orbitals is in the same direction, but smaller. These effects on s and p orbitals increase the shielding of the nuclear charge for d and f electrons; hence the net relativistic effect may be reversed] Le., increased radius and decreased ionization potential. It is well-known that the radii of the lanthanide ions decrease from La to Lu and that this reduction in radius persists for the following elements. This “lanthanide contraction” is cited as the immediate cause of the near equality of radii (in comparable oxidation states) for Hf and Zr, T a and Nb, etc., through Au and Ag and possibly further. The underlying cause is commonly stated as the incomplete shielding of the nucleus by the 14 4f electrons; thus a larger effective core charge contracts the 5p, 5d, 6s orbitals. This is the single most important cause of the contraction. But we shall see that the relativistic equation yields smaller radii than the nonrelativistic equation in some cases. Table I1 gives both the relativistic and nonrelativistic calculated radii for the 5p shell as well as the experimental ionic radii5 for lanthanum and lutetium and for comparison also for yttrium (4p shell). One would not (9) C. E. Moore, “Atomic Energy Levels”, NBS Circular No. 467, Vol. 1-111, U.S. Government Printing Office, Washington, D.C., revised 1971.
Relativistic E f f e c t s
Vol. 12, 1979
273
Table I11 Radii ( ( r ) ,A . ) and Weighted Averages for Relativistic 5d and 6 p real atom nonrelativistic
pseudoatom nonrelativistic
Hf Re Au
Hg
6s 2.484 2.231 2.235 1.984 1.762 1.613 1.499
5d 1.325 1.076 0.912 0.849
T1 Pb Bi
6~
5d 1.179 0.952 0.817 0.758
2.245 1.986 1.805
Table IV Calculated Orbital Energies and Experimental Ionization Potentials in eV for Valence Shell Electrons SI,,
Au, exptl calcd relativ re1 wt av nonrelativ pseudoatom Ag, exptl calcd relativ re1 wt av nonrelativ
9.22 7.94 7.94 6.01 5.18 7.58 6.45 6.45 5.99
d,,, 11.22 11.66
d,,, 12.81 13.43 12.37 14.17 14.62
12.51 13.64
13.18 14.31 13.91 14.62
expect that exact agreement of the experimental ionic radius with the mean value of r for the outer shell of the ion, but there should be a close relationship of relative values. In fact the ionic radius exceeds the average relativistic radius by 0.103 A in all cases. The ionic radius of lutetium is significantly less than that of yttrium. It is also apparent that there is a relativistic contraction which is trivial for yttrium, small for lanthanum, but significant for lutetium. While the relativistic contribution to the total contraction from La to Lu is only about 107'0, it is the relativistic effect that reduces the radius of Lu significantly below that for yttrium. In order to measure the effect of the 4f shell for elements following the lanthanides, nonrelativistic calculations were madelo for pseudoatoms in which the nuclear charge was reduced by 14 units and the 4f orbitals were deleted. These results are compared with the nonrelativistic and the relativistic results for the real atoms in Tables III-V. For the radius of the 6s orbital the contraction caused by the 4f shell decreases through the series Hf to Bi from 0.33 to 0.13 A, while the relativistic effect remains about constant a t 0.2 A. Thus, while both effects have the same general magnitude and the same direction, the relativistic effect becomes the more important for the heavier elements. In the case of the 5d orbitals, however, the relativistic effect is in the opposite direction; the 4f shell contracts the 5d orbital, but relativistic effects expand it. From T1 on, the 6p orbitals begin to be occupied and one finds that the effects on the 6p radii are similar to those on the 6s orbital but of decreased magnitude. Table IV gives energy values for the valence orbitals in gold and silver. The orbital energies calculated on a self-consistent-field basis are only rough approximations to the ionization potentials because electron correlation and relaxation effects are omitted. But with these factors considered, the relativistic values agree well with experiment. Now comparing gold with silver, (10) P. S. Bagus, Y. S. Lee, and K. S. Pitzer, Chem. Phys. Lett., 33, 408 (1975).
6s 2.153 1.955 1.958 1.761 1.570 1.442 1.373
real atom relativistic
6P
5d 1.263 0.992 0.839 0.779
2.078 1.829 1.660
6s 1.955 1.734 1.620 1.515 1.365 1.266 1.187
6P
2.036 1.783 1.614
Table V The Inert Pair Effect: Orbital Energies for Ge, Sn, and Pb (eV) element
Ge
Sn
Pb
s, relativ s, nonrel p, wt av re1 p, nonrel A € , relativ A € , nonrel A e , pseudoatom
15.52 15.16 7.29 7.33 8.23 7.83
13.88 13.04 6.71 6.76 7.17 6.28
15.41 12.49 6.48 6.52 8.93 5.97 4.78
-
-
the s electron is more tightly bound in gold than in silver by 1.5 eV, whereas the d5/, electrons are more loosely bound in gold by about the same amount. But within about 0.5 eV the nonrelativistic values for gold or pseudogold are the same as those for silver where relativistic effects are not very large. Thus this large shift toward more strongly bound s and more loosely bound d electrons is primarily a relativistic effect. But these shifts explain very well the differences in chemical behavior. With the high ionization potential for the 6s electron even in the large atom, gold is very difficult to oxidize. But in compounds it forms several strong covalent bonds since 5d orbitals can be involved as well as 6s and 6p. Not only is the difference in energy between d and s orbitals smaller in gold than in silver but the differences in radii are smaller also. This tendency toward strong covalent bonds is also shown in the diatomic molecule Au, whose dissociation energy,112.29 eV, exceeds that of either Ag, (1.65 eV) or Cu, (1.95 eV). Also note the trend in Do down from Cu, to Ag,, which is a normal pattern, and then anomalously up to A u ~An extensive theoretical study has been madel, for Au, which is discussed below. The electron affinities of these atoms are13 Cu 1.226 eV, Ag 1.202 eV, and Au 2.30B6 eV; again the anomaly for gold is striking and is understandable from the relativistic effect in contracting the 6s orbital and making it more strongly bound. The compounds CsAu and RbAu are unusual in being nonmetallic semicond~ctors'~ with the CsCl structure. They are presumably based on an ionic M+Au- model, and the high electron affinity of gold is essential t o their nonmetallic character. In the case of mercury the combined relativistic and 4f-shell effect contracts the 6s orbital and strengthens (11) K. A. Gingerich, J. Cryst. Growth, 9, 31 (1971); J. Kordis, K. A. Gingerich, and R. J. Seyse, J . Chem. Phys., 61, 5114 (1974). (12) Y. S.Lee, W. C. Ermler, K. S.Pitzer, and A. D. McLean, J.Chem. Phys., 70,288 (1979); W. C. Ermler, Y. S.Lee, and K. S.Pitzer, ibid.,70, 293 (1979). (13) H. Hotop, R. A. Bennett, and W. C. Lineberger, J . Chem. Phys., 58, 2373 (1973); H. Hotop and W. C. Lineberger, ibid., 58, 2379 (1973). (14) W. E. Spicer, A. H. Sommer, and J. G. White, Phys. Reu., 115, 57 (1959).
Pitzer
274
Accounts of Chemical Research
Table VI Valence Orbital Energies (eV) and Radii ( A ) for Uranium
5f E , 6d E , 7s (r?, 5f ( r ) ,6 d ( r ? ,7s E,
relativ wt av
nonrelativ
9.01 5.09 5.51 0.76 1.71 2.30
17.26 7.25 4.54 0.67 1.52 2.67
its bonding capacity, as was the case in gold. Thus mercury is a more noble metal than zinc or cadmium and its compounds show stronger covalent bonding. The unexpected volatility of mercury arises from the increase in 6s to 6p promotion energy as compared to zinc and cadmium. The unusual dimeric, dipositive ion HgZ2+is isoelectronic with Au2, and we have already noted the anomaly in the strength of the bond in Au2 which will be shown later to be primarily of relativistic origin. The 5d orbitals play a lesser and the 6p orbitals a greater role in mercury than in gold; the relativistic and 4f-shell effects on radii are shown in Table 111. In summary, the anomalous properties of mercury arise from the sum of relativistic and 4f-shell contributions which are of comparable magnitude and reinforce one another in most respects. The appearance of compounds, primarily in groups 4 through 7, with oxidation number two less than the group number is ascribed to an “inert pair” of s electrons. This effect is enhanced for the 6s, 6p valence shell and is extended to thallium in group 3. Thus the energy required to remove the 6s pair of electrons is much greater for T1, Pb, and Bi than for the 5s pair in In, Sn, and Sb. The pertinent atomic orbital energies for Ge, Sn, and P b are given in Table V. On a nonrelativistic basis, even with the effect of the 4f shell, all of the energies decrease along this sequence and no grossly anomalous trend is indicated. But on a relativistic basis, the s electron in P b is bound as strongly as in Ge and much more than in Sn, while the normal trend is maintained for the weighted average for the p electrons. Thus the difference in binding for s as compared to p electrons shows a very anomalous trend from Sn to Pb. Although the 4f shell effect is in the same direction, as indicated by the value for pseudolead, the major part of the anomaly arises from relativity in this case. The data for the third or fifth group show the same pattern. There is also an enhanced inert pair effect for the elements Ge through Br as compared to those of the elements in the rows above and below, but this is not a relativistic effect; rather it is associated with the introduction of the first d shell. Just as in the case of the 4f shell in the lanthanides, the shielding of 4s and 4p electrons by the 3d shell is incomplete and less complete for s than for p orbitals. Hence the orbital energies are increased more for 4s than for 4p and the inert pair effect is enhanced in relation to expectations related in part to elements Si through C1. In various discussions15J6of the bonding in the uranyl ion, it is suggested that this unique ion has its great stability because 5f, 6d, 7s, and 7p orbitals can all contribute to the remarkably short and strong U-0 (15) R. E. Connick and 2. 2. Hugus, Jr., J . Am. Chem. SOC.,74, 6012 (1952). (16) C. Y. Yang, K. H. Johnson, and J . A. Horsley, J . Chem. P h p . , 68, 1001 (1978), and references cited therein.
Table VI1 Dirac Atomic Orbitalsa s,,
’, m = + ‘ I z
s,,~,
p l i 2 ,m = f112
-
p3,’, m = ’ I 2 [;(r) sin e e - @
P112,
1
m = - ‘I2
m = -‘I?
P ~ ,m~ =, - 312 [O
3
g ( r ) sin 6 e-’@ f ( r ) sin2 e e-‘;@ - f ( r ) sin e cos 6 e - @ P ~ , m~ =, - ’ I 2
f ( r ) sin e cos e eio f ( r ) sin’ e e Z i Q P ~ , m~ =, t i l 2
a The angular factors are shown explicitly; other factors are included in g ( r ) and f ( r ) in each case.
bonds. Clearly the mean radius of the 5f orbital is much less than that for the others, but in contrast to the 4f orbital, the 5f has a radial node and has significant amplitude a t radii much beyond the average. From Table VI it is clear that relativistic effects substantially narrow the ranges of orbital energies and radii from 5f through 7s. Thus it is reasonable to conclude that special properties of oxidation state VI for U, Np, and P u arise at least in large part because of the relativistic effects in making 7s (and 7p) orbitals more compact and strongly bound while making 5f orbitals larger and much more loosely bound. We have now shown that most of the anomalous properties of various heavy elements are to be ascribed in substantial part to relativistic effects and that this conclusion can be based on simple arguments from atomic radii and orbital energies (or ionization potentials). In a few situations it is important, however, to recognize differences in the bonding characteristics of relativistic orbitals, especially p orbitals. Bonding Characteristics of Relativistic Orbitals While Schrodinger wavefunctions are ordinary scalar functions, Dirac orbitalslJs are fourth-order vectors. The electron probability density is given by the sum of the squares (in absolute magnitude) of the four components. Two of these components vanish in the nonrelativistic limit c a; these are called “small components” and are always very small in the outer portion of an atom but may become important near the nucleus. The other two “large components” can be thought to correspond to the Schrodinger wavefunctions for + and - spin, respectively, and it is these functions that must be considered in estimating the bonding characteristics. Powellli has given a simple and clear description of relativistic orbitals for atoms where various properties are discussed. The angular properties of orbitals are especially important for chemical bonding, and these are shown for s ~ ,p112, ~ , and ~ 3 1 orbitals 2 in Table VII.
-
(17) R. E. Powell, J. Chem. Educ., 45, 558 (1968).
Vol. 12, 1979
Relativistic Effects
Here various factors are included within the functions g(r) and f ( r ) which are eigenfunctions of the radial equations for the particular atom and principal quantum number. The large components are listed first with the factor g(r);the small components in third and fourth places with the factor f ( r ) . As one can see from Table VII, the angular properties of s orbitals are unchanged by relativity. The large components have no angular dependence, Le., are spherical, and only the first or the second component is non-zero. Thus they can form strong bonds in any direction. The only significant relativistic effect on s orbitals is the quantitative change in g(r) whereby they are contracted and more tightly bound. This increases the strength of bonds based on s orbitals. In contrast, there are profound differences in angular properties for those relativistic p orbitals with z component of angular momentum m = fl/% Both large components are non-zero, and one component has the angular dependence of a pa orbital whereas the other has that of a pir orbital. If one forms a diatomic molecular orbital from p1p atomic orbitals for each atom with signs appropriate for a bonding, then the other components yield ir antibonding. More exactly, if the plj2 orbitals are combined with g symmetry one has one-third a-bond and two-thirds A-antibond character. Correspondingly, the combination with u symmetry yields one-third a-antibond and two-thirds ir-bond character. Thus p1/2 orbitals do not form strong bonds. By taking linear combinations of pl/2and p3/2 orbitals, the angular and bonding characteristics of Schrodinger p orbitals can be regained, but this requires substantial promotion energy in many cases. This relativistic effect for p bonding should be most prominent for Tlz where the atom has a single pljz valence electron. Tl2 is very weakly bound; indeed its bond energy is still uncertain.18 In T1H this effect will be less severe since the hydrogen contributes an s orbital to the bond. With negligible A interaction from the hydrogen, the r-antibonding effect is unimportant, and it is only the reduced a-bonding effect of a pljn orbital (as compared to a nonrelativistic p orbital) that remains. In some exploratory c a l ~ u l a t i o n sI ~made ~ the very crude assumption of full promotion of pljz electrons or p3/z vacancies to the nonrelativistic 2 ) + ‘/3(p3/2) combinations for optimum bonding. 6f course, in reality the bonding molecular orbitals will involve a compromise with partial promotion and somewhat weaker bonding than would correspond to the llq(pljz) + 2/3(p3/2)combination, but as yet there is no simple method of estimation for the intermediate state. More complex calculations20,21 of the types discussed in the next section indicate that the proportion of pl/z and p3l2 participation in T1H is about 60% pl/z and 40% p3I2. This is evidently a compromise between the 100% pljz for minimum energy of the T1 atom and the 33% pl/2 for optimum bonding. On the basis of simplified calculations assuming the full promotion energy to ‘ / 3 ( ~ 1 , 2 ) + 2 / 3 (p3/2)orbitals, (18)J. Drowart and R. E. Honig, J. Phys. Chem., 61,980 (1957); S. A,, Shuchukarev, G. A. Semenov, and I. A. Rat’kovskii, J . Inorg. Chem. USSR, 7,240 (1962); D. S. Ginter, M. L. Ginter, and K. K. Innes, J . Phys. Chem., 69, 2480 (1965). (19) K. S. Pitzer, J. Chem. Phys., 63, 1032 (1975). (20) P. Pyykko and J. P. Desclaux, Chem. Phys. Lett., 42, 545 (1976). (21) Y. S. Lee, to be published.
275 Table VI11 Properties of Au,
a
state
Re, A
D e , eV
Te,eV
X Og+,calcd exptla A Og+,calcd exptla B Ou+, calcd exptla
2.37 2.47 2.51 2.57 2.50 2.51
2.27 2.31b 0.79 1.00
0 0 2.61 2.44 3.55
From ref 26.
1.38 1.78
3.18
From ref 11.
it was estimatedlgthat elements 112,114, and 118 would be relatively stable as atoms and approach “inert gas” (actually inert volatile liquid) characteristics. Also it was suggested22that radon fluoride may be an ionic compound (Rn+F- or Rn2+F-,) rather than a covalently bonded structure and that element 118 would show an even stronger tendency in that direction. Refined calculations would change the numerical values, but it is not likely that the qualitative indications would be changed. Finally, it may be noted that similar problems arise for bonding with relativistic d or f orbitals in relation to their angular properties, but it is not yet clear what the impact is on chemical properties. This matter deserves future study. Relativistic Calculations for Molecules A full exact relativistic treatment of electronic motion in a molecule is very difficult, and none has been completed for a molecule which includes heavy, many-electron atoms where the effects we have been considering are chemically significant. But approximate calculations of useful accuracy have been made on two different bases. One method12-23-25 assumes that the core electrons remain unchanged in molecule formation and replaces their detailed influence on valence electrons by effective potentials. This method was used to treat diatomic gold12 with the results shown in Table VIII, which show that the of the two excited spectroscopic states which have been observed as well as those of the ground state are obtained with useful accuracy from the relativistic calculations. Comparison with nonrelativistic calculations for the ground state indicates that the relativistic effects strengthen the bond by 1.0 eV and shorten it by 0.35 A. The anomalous trend in dissociation energies in the series Cu2,Ag,, Auz was stated above; if the bond energy in Auz is decreased by 1.0 eV, the anomaly disappears. Thus the anomaly is primarily caused by the relativistic effects. Another approximation for relativistic molecular calculations is the one-center method of Desclaux and Pyykko.20>27Here all electrons are considered, but only in orbitals centered on the heavy atom. The method gives useful results for compounds of a single heavy atom with hydrogen; there are only valence electrons in the vicinity of the protons. These one-center cal(22) K. S. Pitzer, J . Chem. Soc., Chem. Commun., 760 (1975). (23) Y. S. Lee, W. C. Ermler, and K. S. Pitzer, J. Chem. Phys., 67,5861 (1977): 69. 976 11978). (24) P. J. Hay, W. R. Wadt, L. R. Kahn, and F. W. Bobrowicz, J. Chem. Phys., 69, 984 (1978). (25) G. Das and A. C. Wahl, J . Chem. Phys., 64, 4672 (1976). (26) L. L. Ames and R. F. Barrow, Trans. Faraday Soc., 63,39 (1967). (27) J. P. Desclaux and P. Pyykko, Chem. Phys. Lett., 29,534 (1974); 39, 300 (1976); revised values by private communication.
Pyykko and Desclaux
276 Table IX Molecular Constants for AuH
R e , calcd nonrel, A calcd relativ, A exptl, A D e , calcd relativ, eV exptl, eV a Effective potential method. 24 Experimental.”
Accounts of Chemical Research
is sometimes ignored by others. The very strong spectral line of mercury at 2537 A is a “spin-forbidden’’ 3P1 ‘Sotransition. The intensity of this line is a vivid reminder that spin is not separately quantized in heavy atoms. The magnetic properties and the related splittings in the spectra of many compounds involving heavy atoms were initially interpreted with appropriate consideration of spin-orbit energies. For example, Moffitt et al.29 showed that the spectra of the molecules ReF6 to PtF6 are closer to j-j coupling than to L-S coupling but that ligand field effects are even more important. Since most of the literature presently gives full consideration to the relativistic (spin-orbit) effects for these properties, there is no need for further comment here.
-
1.807,a 1.747’
1.522,a 1.622’ 1.524c 2.66a 3.37c
’One-center method.*’
culations can be made relativistically as well as nonrelativistically, and the difference may give a useful measure of the relativistic effect even where the absolute value of the calculated property is not very accurate. Other approximate calculations including relativistic features are reviewed by P y ~ k k o . ~ It is interesting to compare the relativistic effects in AuH with those in Au2. There are effective potential calculations of Hay et al.24and one-center calculations of Desclaux and P ~ y k k which o ~ ~ are given in Table IX together with experimental values.28 The effective potential method yields excellent agreement with experiment for the bond distance, with a relativistic shortening of 0.28 A as compared to 0.35 A in Au2.
Direct Consequences of Spin-Orbit Energies In addition to the effects on bond energies, there are other consequences when spin-orbit energies become large. Cotton and Wilkinson5 discuss the relationship of spin-orbit coupling to magnetic properties. If the spin-orbit splitting becomes large as compared to thermal energy, paramagnetic effects can be largely suppressed. Another very important consequence is the breakdown of spin selection rules and the enhancement of rates of singlet-triplet interconversion. This is well-known to those working with heavy elements but (28) B. Rosen, “Spectroscopic Data Relative to Diatomic Molecules”, Pergamon Press, Oxford, 1970.
Summary While spin-orbit effects have been recognized in interpreting magnetic properties of molecules containing heavy atoms, more elaborate calculations are required to establish the contribution of relativistic terms to bond energies, ionization potentials, and various chemical properties. Relativistic quantum mechanical calculations have now been made for atoms and for a few molecules, and one can show that many of the anomalous departures from periodic table trends for heavy atoms can be attributed to relativistic effects. T h e research reviewed i n this Account received support f r o m t h e Energy Research and Development Administration and t h e Division of Chemical Sciences, Office of Basic Energy Sciences, U.S. D e p a r t m e n t of Energy, and was carried out i n p a r t i n cooperation w i t h I.B.M. Laboratories. I gratefully acknowledge the contributions of m y collaborators, Y. S. Lee, P. S. Bagus, W. C . Ermler, a n d A. D . M c L e a n , and valuable discussions w i t h Professor N . Bartlett. (29) W. Moffitt, G. L. Goodman, M. Fred, and B. Weinstock, Mol. Phys., 2, 109 (1959); see also B. Weinstock, Chem. Eng. News, 42, 86 (Sept 21, 1964).
Relativity and the Periodic System of Elements PEKKA PYYKKO* Department of Physical Chemistry, Abo Akademi, SF-20500 Abo (Turku), Finland
JEAK-PAUL DESCLAUX Departement de Recherche Fondamentale, Chimie Physique Nuclfiaire, Centre d’Etudes Nuclgaires de Grenoble, 85 X , F-38041 Grenoble Cfidex, France Received November 30. 1978
We live in a world with a finite speed of light, c. Yet, most of the existing theoretical chemistry refers to an Pekka Pyykko was born in Hinnerjoki, Finland, in 1941. He obtained his Fii.Kand., FiLLic.. and Ph.D. from the University of Turku. After working at the Universities of Aarhus, Goteborg, Helsinki, Jyvaskyia, Paris XI, and Ouiu in 1968-1974, he returned to Turku as Associate Professor of Quantum Chemistry at Abo Akademi. His main interests are NMR theory and, since 1970, relativistic quantum chemistry. Jean-Paul Desclaux was born in Paris in 1939. He attended &ole Nationaie des T616communications and became Docteur 6s Sciences Physiques at the University of Paris. He has worked for the French Commissariat B I’hergie Atomique since 1966. After 2 years at Institut Laue-Langevin in Grenoble in 1974-1975, he has been at the Centre d’gtudes Nucl6aires de Grenoble. His main interests are in relativistic atomic calculations.
0001-4842/79/0112-0276$01.00/0
imaginary world where c would be infinite. In the following we define relativistic effects as the difference between these two cases. The essential point of the present Account is that these effects seem to explain some of the most conspicuous chemical anomalies in the latter half of the periodic system. Examples of these are: Why is gold yellow and noble? Indeed, why is it different from silver at all? Why is mercury a liquid? What causes its strong tendency for two-coordination? Why is the mercurous ion so stable? How can one explain the valency change from I11 for
0 1979 American Chemical Society
